How to move the 3D manipulator widget itself
Most likely the origin of your object is off. To recenter it, select the object and press &#9096; Ctrl&#9095; Alt&#8679; ShiftC> Origin to geometry. 

If you want to move it to a more customized location, you can move the 3D cursor where you want it to go, either by clicking with  LMB or by snapping the cursor with &#8679; ShiftS, then pressing &#9096; Ctrl&#9095; Alt&#8679; ShiftC> Origin to 3D cursor.

Note that the manipulator widget is located at the pivot point, which is set in the header of the 3D view:



It's also possible that the pivot point is set to 3D cursor (.), in which case the manipulator will be position at the cursor. To switch it back to the default setting of median point, either select it in the drop down or press &#9096; Ctrl, (comma).